On a class of vector fields with discontinuity of divide-by-zero type and its applications

Roberta Ghezzi; Alexey Remizov

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arXiv · 1007.0912

On a class of vector fields with discontinuity of divide-by-zero type and its applications

Roberta Ghezzi·Alexey Remizov

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Abstract

We study phase portraits and singular points of vector fields of a special type, that is, vector fields whose components are fractions with a common denominator vanishing on a smooth regular hypersurface in the phase space. We assume also some additional conditions, which are fulfilled, for instance, if the vector field is divergence-free. This problem is motivated by a large number of applications. In this paper, we consider three of them in the framework of differential geometry: singularities of geodesic flows in various singular metrics on surfaces.

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Roberta Ghezzi, Alexey Remizov. 2010-07-06. On a class of vector fields with discontinuity of divide-by-zero type and its applications. https://arxiv.org/abs/1007.0912

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